cp's OEIS Frontend

A338171 a(n) is the sum of those divisors d of n such that tau(d) divides sigma(d).

%I A338171 #24 Sep 09 2024 14:52:47
%S A338171 1,1,4,1,6,10,8,1,4,6,12,10,14,22,24,1,18,10,20,26,32,34,24,10,6,14,
%T A338171 31,22,30,60,32,1,48,18,48,10,38,58,56,26,42,94,44,78,69,70,48,10,57,
%U A338171 6,72,14,54,91,72,78,80,30,60,140,62,94,32,1,84,142,68,86
%N A338171 a(n) is the sum of those divisors d of n such that tau(d) divides sigma(d).
%C A338171 a(n) is the sum of arithmetic divisors d of n.
%C A338171 a(n) = sigma(n) = A000203(n) for numbers n from A334420.
%C A338171 See A338170 and A338172 for number and product such divisors.
%H A338171 Robert Israel, <a href="/A338171/b338171.txt">Table of n, a(n) for n = 1..10000</a>
%F A338171 a(p) = p + 1 for odd primes p (A065091).
%e A338171 a(6) = 10 because there are 3 arithmetic divisors of 6 (1, 3 and 6): sigma(1)/tau(1) =  1/1 = 1; sigma(3)/tau(3) = 4/2 = 2; sigma(6)/tau(6) = 12/4 = 3. Sum of this divisors is 10.
%p A338171 f:= proc(n) uses numtheory;
%p A338171 convert(select(t -> sigma(t) mod tau(t) = 0, divisors(n)),`+`) end proc:
%p A338171 map(f, [$1..100]); # _Robert Israel_, Oct 27 2020
%t A338171 a[n_] := DivisorSum[n, # &, Divisible[DivisorSigma[1, #], DivisorSigma[0, #]] &]; Array[a, 100] (* _Amiram Eldar_, Oct 15 2020 *)
%o A338171 (Magma)  [&+[d: d in Divisors(n) | IsIntegral(&+Divisors(d) / #Divisors(d))]: n in [1..100]];
%o A338171 (PARI) a(n) = sumdiv(n, d, d*!(sigma(d) % numdiv(d))); \\ _Michel Marcus_, Oct 15 2020
%Y A338171 Cf. A000005 (tau), A000203 (sigma), A003601 (arithmetic numbers).
%Y A338171 Cf. A334420, A334421.
%K A338171 nonn,look
%O A338171 1,3
%A A338171 _Jaroslav Krizek_, Oct 14 2020